Food Allergies Treatment

I was on a low carb diet and did not eat any breads for the past month and I felt great! My stomach pains, bloating, and constipation, and lethargy went away. As soon as I began introducing bread in small amounts back into my diet, I started to get the same symptoms again that I have had my whole life. I am thinking it is an allergy or intolerance. I have talked to my doctor in the past and she said to try an elimination diet to see what is bothering me…which I did.
Are there tests that say which it is?

My son is almost 7 weeks old and has been VERY gassy since about 2 weeks old. This is extremely painful for him and he is fussy because of it. It is also painful for him to poop. We have tried gripe water and mylicon…none of it helped.
We have him on probiotics and are taking him to the chiropractor. This seemed to be helping but he has now gotten worse the last 2-3 days. I’ve been reading about milk protein intolerance/allergy.
What is the difference? What are the symptoms? From what I’ve seen, symptoms often include some kind of rash or blood in stools. He has never had any of this…just horrible, painful gas. He does spit up a lot too, which has gotten worse. I’ve wondered about reflux but know that has nothing to do with the gas.
Is it possible he has a milk protein intolerance or allergy without the other symptoms? Just the gas and spitting up.
I am breastfeeding. If this is a likely possibility, I will cut dairy out of my diet. But if there is no chance this is a possibility, I don’t want to deprive him and me of those nutrients.